Diffractive optical element and scanning optical apparatus using the same

ABSTRACT

Diffraction optical element used in a scanning optical apparatus as a scanning optical element has a diffraction grating formed on a substrate. The diffraction grating has a tilt portion for generating a power and a wall portion connecting one end portion of the tilt portion to the substrate. The wall portion is tilted within a predetermined range with respect to a normal of the substrate surface. The tilt angle of the wall portion of the diffraction grating with respect to the normal of the substrate continuously changes to increase as a distance away from an optical axis of the diffraction optical element becomes large.

BACKGROUND OF THE INVENTION

1. Field of the invention

The present invention relates to a diffractive optical element andscanning optical apparatus using the same and, more particularly, to anapparatus which records image information by causing a deflectionelement to deflect a light beam emitted by a light source means formedfrom a semiconductor laser and optically scanning a surface to bescanned through a scanning optical element (imaging element) having f-θcharacteristics, and is suitable for an image forming apparatus such asa laser beam printer (LBP) or digital copying machine having anelectrophotography process.

2. Related Background Art

In a conventional scanning optical apparatus used in a laser beamprinter, digital copying machine, or the like, a light beam which isoptically modulated in accordance with an image signal and is outputfrom a light source means is periodically deflected by an opticaldeflector such as a rotary polyhedral mirror (polygon mirror), and isfocused to form a beam spot on the surface of a photosensitive recordingmedium (photosensitive drum) by a scanning optical element (imagingelement) having f-θ characteristics. Then, the beam spot is scanned onthat surface to record an image.

FIG. 1 is a schematic sectional view showing principal part of aconventional scanning optical apparatus of this type.

Referring to FIG. 1, a divergent light beam emitted by a light sourcemeans 91 is converted into a nearly collimated light beam by acollimator lens 92, and the light beam (light amount) is limited by astop 93. Then, the light beam enters a cylinder lens (cylindrical lens)94 having a predetermined power in only the sub-scanning directionperpendicular to the drawing surface. Of the nearly collimated lightbeam that enters the cylinder lens 94, light components in the mainscanning section directly emerge as a nearly collimated light beam. Inthe sub-scanning section perpendicular to the drawing surface, lightcomponents are focused to form a nearly linear image on a deflectionsurface (reflection surface) 95 a of an optical deflector 95 thatcomprises a rotary polyhedral mirror (polygon mirror).

The light beam deflected and reflected by the deflection surface 95 a ofthe optical deflector 95 is guided onto a photosensitive drum surface 98as a surface to be scanned via a scanning optical element (f-θ lens) 96having f-θ characteristics. By rotating the optical deflector 95 in thedirection of an arrow A, the light beam scans the photosensitive drumsurface 98 in the direction of an arrow B. In this way, an image isrecorded on the photosensitive drum surface 98 as a recording medium.

Conventionally, various scanning optical apparatuses using plasticlenses have been proposed as scanning optical systems because of theircapability of highly accurate aberration correction using asphericalsurfaces and cost reduction by injection molding.

However, a plastic lens largely changes in its aberration (especiallyerrors in focus or magnification) due to environmental variations. Thisposes a serious problem in a scanning optical apparatus having a smallspot diameter.

Recently, to compensate for aberration variations unique to a plasticlens, some apparatuses have been equipped with diffractive opticalelements as a scanning optical system, as proposed in, e.g., JapanesePatent Application Laid-Open No. 10-68903. In this prior art, forexample, when ambient temperature increases, chromatic aberration isgenerated using a diffractive optical element in advance so as tocompensate for a change in aberration due to a decrease in refractiveindex of a plastic lens with a change in aberration due to wavelengthvariation of a semiconductor laser as a light source. When a diffractiveoptical element is used singly, the element has a predeterminedthickness. Hence, the element manufactured by injection molding isexcellent in molding properties.

A diffractive optical element is very useful as the optical system of ascanning optical apparatus. However, the light utilization efficiency(to be referred to as a diffraction efficiency η hereinafter) of adiffractive optical element changes depending on conditions, unlike arefractive optical element. This will be described below using adiffraction grating model.

FIG. 2 is an explanatory view of a diffraction grating-model. Thisdiffraction grating model comprises a continuous grating having agrating pitch of P μm and a grating depth of h μm. The ratio of thegrating pitch to the grating depth is called an aspect ratio AR, and itis defined that AR=grating pitch P/grating depth h. A light beamincident on the substrate of the diffraction grating model at an angleof incidence θi is diffracted and emerges in the direction of designeddiffraction order.

FIG. 3 is an explanatory view showing the dependence of the diffractionefficiency on the angle of incidence when the aspect ratio AR is 4 inthe above diffraction grating model. As is apparent from FIG. 3, thediffraction efficiency greatly changes depending on the angle ofincidence, and especially, the diffraction efficiency of a light beamincident at a large angle of incidence lowers.

FIG. 4 is an explanatory view showing the dependence of the diffractionefficiency on the aspect ratio when the angle of incidence on thegrating portion is θi=0 in the above diffraction grating model. In FIG.4, the grating depth h is not changed while the aspect ratio AR ischanged by changing the grating pitch P. When the aspect ratio is lowerthan 4, the diffraction efficiency abruptly decreases.

As is apparent from the above two conditions, when a diffractive opticalelement is used as the scanning optical system of a scanning opticalapparatus, the diffraction efficiency lowers in the off-axis regionwhere the angle of incidence is large and the aspect ratio is low, sothe uniformity of an image plane illuminance on a surface to be scanneddegrades.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a diffractiveoptical element suitable for high-resolution printing, which suppressesa decrease in diffraction efficiency of the diffractive optical element,especially in the off-axis region, increases the uniformity of imageplane illuminance on a surface to be scanned, and minimizes aberrationchanges due to various variations, without increasing cost, with asimple arrangement in which a diffraction grating comprises a tiltportion for mainly generating a power and a wall portion connecting oneend portion of the tilt portion to a substrate, and the wall portion istilted with respect to a normal to the substrate, and a scanning opticalapparatus using this diffractive optical element.

A diffractive optical element according to the present invention, whichhas a diffraction grating formed on a substrate surface and diffracts anincident light beam to obtain a predetermined power, is characterized inthat

the diffraction grating has a tilt portion for generating a power and awall portion connecting one end portion of the tilt portion to thesubstrate, and

the wall portion is tilted with respect to a normal to the substratesurface to increase the diffraction efficiency at that portion.

Especially, the element is characterized in that

the tilt angle θe of the wall portion of the diffraction grating withrespect to the normal to the substrate surface satisfies

tan⁻¹(h/P)≦θe≦tan⁻¹(h/P)+10°

 where h is the depth of the diffraction grating, and P is the gratingpitch,

the tilt angle θe of the wall portion of the diffraction grating withrespect to the normal to the substrate surface continuously changes toincrease as a distance away from an optical axis of the diffractiveoptical element becomes large,

the diffractive optical element is manufactured by forming thediffraction grating on a glass substrate by a replica process, and

the diffractive optical element is manufactured by integrally formingthe substrate and the diffraction grating from a plastic material byinjection molding.

A scanning optical apparatus according to the present invention, whichconverts a light beam emitted by a light source into a substantiallycollimated light beam by a conversion optical element, deflects theconverted substantially collimated light beam with a deflection element,and forms an image of the light beam deflected by the deflectionelement, through a scanning optical element, on a surface to be scannedso as to scan the surface, is characterized in that

the scanning optical element comprises at least one refractive opticalelement and at least one diffractive optical element having adiffraction grating, the diffraction grating being formed on a substratesurface and having a tilt portion for generating a power and a wallportion connecting one end portion of the tilt portion to the substrate,and the wall portion being tilted with respect to a normal to thesubstrate surface.

Especially, the apparatus is characterized in that

the diffraction grating is formed on a side of the surface to be scannedof the diffractive optical element,

a tilt angle θe of the wall portion of the diffraction grating withrespect to the normal to the substrate surface satisfies

tan⁻¹(h/P)≦θe≦tan⁻¹(h/P)+10°

 where h is a depth of the diffraction grating, and P is a gratingpitch,

a tilt angle θe of the wall portion of the diffraction grating withrespect to the normal to the substrate surface continuously changes toincrease as a distance from an optical axis of the diffractive opticalelement becomes large,

the diffractive optical element is manufactured by forming thediffraction grating on a glass substrate by a replica process,

the diffractive optical element is manufactured by integrally formingthe substrate and the diffraction grating from a plastic material byinjection molding,

the diffractive optical element has different powers in main scanningand sub-scanning directions,

the refractive optical element comprises a toric lens made of a plasticand having different powers in main scanning and sub-scanningdirections, and

the substrate surface comprises a flat surface or a curved surface.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view showing the principal part of a conventionalscanning optical apparatus in the main scanning direction;

FIG. 2 is an explanatory view showing a grating model of a conventionaldiffractive optical element;

FIG. 3 is an explanatory view showing the dependence of the diffractionefficiency of the conventional diffractive optical element on the angleof incidence;

FIG. 4 is an explanatory view showing the dependence of the diffractionefficiency of the conventional diffractive optical element on the aspectratio;

FIG. 5 is a schematic view showing a principal part of a scanningoptical apparatus according to the first embodiment of the presentinvention;

FIG. 6 is a sectional view showing a principal part of the opticalsystem of the scanning optical apparatus shown in FIG. 5 in the mainscanning direction;

FIG. 7 is an enlarged explanatory view showing a diffractive opticalelement of the first embodiment of the present invention in the mainscanning direction;

FIG. 8 is an explanatory view showing the diffraction efficiency of thediffractive optical element of the first embodiment of the presentinvention;

FIG. 9 is an enlarged explanatory view showing a diffractive opticalelement of the second embodiment of the present invention in the mainscanning direction;

FIG. 10 is an explanatory view showing the diffraction efficiency of thediffractive optical element of the second embodiment of the presentinvention;

FIG. 11 is a schematic view showing a principal part of a scanningoptical apparatus according to the third embodiment of the presentinvention; and

FIG. 12 is an enlarged explanatory view showing a diffractive opticalelement of the third embodiment of the present invention in the mainscanning direction.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 5 is a schematic view showing principal part of a scanning opticalapparatus according to the first embodiment of the present invention.FIG. 6 is a sectional view showing a principal part of the opticalsystem of the scanning optical apparatus shown in FIG. 5 in the mainscanning direction. The grating portion of a diffractive optical element(to be described later) is exaggerated and has a shape different fromthe actual shape.

Referring to FIGS. 5 and 6, a light source means 1 comprises, e.g., asemiconductor laser. A conversion optical element 2 (collimator lens)converts a light beam emitted by the light source means 1 into a nearlycollimated light beam. An aperture stop 3 limits a light beam (lightamount) that passes through it. A cylindrical lens (cylinder lens) 4 hasa predetermined power in only the sub-scanning direction perpendicularto the drawing surface of FIG. 6 and forms a nearly linear image of thelight beam passing through the aperture stop 3 on the deflection surfaceof an optical deflector (to be described later) in the sub-scanningsection.

An optical deflector 5 is formed from, e.g., a polygon mirror (rotarypolyhedral mirror) as a deflection element and rotated by a drivingmeans such as a motor (not shown) in the direction of an arrow A inFIGS. 5 and 6.

A scanning optical element 6 with f-θ characteristics has at least onerefractive optical element and at least one diffractive optical element.The refractive optical element is formed from a single toric lens 61made of a plastic and having different powers in the main scanning andsub-scanning directions. The two lens surfaces of the toric lens 61 inthe main scanning direction have aspherical shapes. The diffractiveoptical element is formed from an elongated diffractive optical element62 having different powers in the main scanning and sub-scanningdirections. A diffraction grating is formed on a substrate surface. Thediffraction grating is formed on a surface of the diffractive opticalelement 62 on a photosensitive drum surface (surface to be scanned) 8side. The substrate surface is flat. The diffraction grating of thediffractive optical element 62 of this embodiment has a tilt portion formainly generating a power and a wall portion connecting one end portionof the tilt portion to the substrate. The wall portion is tilted withrespect to the normal to the substrate surface. For the diffractiveoptical element 62 of this embodiment, the substrate and diffractiongrating are integrally formed from a plastic material by injectionmolding. However, the present invention is not limited to this, and adiffraction grating may be manufactured on a glass substrate by areplica process to obtain the same effect. The toric lens 61 is disposedon the optical deflector 5 side of the middle point between the rotatingshaft of the optical deflector 5 and the photosensitive drum surface 8,and the diffractive optical element 62 is disposed on the photosensitivedrum surface 8 side. The scanning optical element 6 forms an image of alight beam based on image information and deflected by the opticaldeflector 5 on the photosensitive drum surface 8 and corrects any tiltof the deflection surface of the optical deflector 5.

In this embodiment, a divergent light beam emitted by the semiconductorlaser 1 is converted into an almost collimated light beam by theconversion optical element 2. The light beam (light amount) is limitedby the aperture stop 3 and enters the cylindrical lens 4. Of the lightbeam incident on the cylindrical lens 4, light components in the mainscanning cross-section are directly output in the collimated state. Inthe sub-scanning cross-section, the light beam is focused to form analmost linear image (linear image long in the main scanning direction)on a deflection surface 5 aof the optical deflector 5. The light beamdeflected by the deflection surface 5 a of the optical deflector 5 isguided onto the photosensitive drum surface 8 through the scanningoptical element 6. When the optical deflector 5 is rotated in thedirection of the arrow A, the light beam scans the photosensitive drumsurface 8 in the direction indicated by an arrow B. In this fashion, animage is recorded on the photosensitive drum surface 8 as a recordingmedium.

In this embodiment, the toric lens 61 and diffractive optical element 62of the scanning optical element 6 respectively have the followingshapes.

(1) Toric lens: aspherical shape whose main scanning direction can berepresented by a function up to 10th order.

The intersection between the toric lens and optical axis is defined asthe origin. The X-axis is set along the optical axis direction, theY-axis is set along an axis perpendicular to the optical axis in themain scanning section, and the Z-axis is set along an axis perpendicularto the optical axis in the sub-scanning section. At this time, thegenerating-line direction corresponding to the main scanning directionis given by$x = {\frac{Y^{2}/R}{1 + \left( {1 - {\left( {1 + K} \right)\left( {Y/R} \right)^{2}}} \right)^{1/2}} + {B_{4}Y^{4}} + {B_{6}Y^{6}} + {B_{8}Y^{8}} + {B_{10}Y^{10}}}$

(where R is the radius of curvature, and K, B₄, B₆, B₈, and B₁₀ areaspherical coefficients)

The meridian-line direction corresponding to the sub-scanning direction(direction having the optical axis and perpendicular to the mainscanning direction) is given by$S = \frac{Z^{2}/r}{1 + \left( {1 - \left( {Z/r^{\prime}} \right)^{2}} \right)^{1/2}}$

for r′=r₀(1+D₂Y²+D₄Y⁴+D₆Y⁶+D₈Y⁸+D₁₀Y¹⁰) (where r₀ is the meridian-lineradius of curvature on the optical axis, and D₂, D₄, D₆, D₈, and D₁₀ areaspherical coefficients)

(2) Diffractive optical element: diffraction surface whose main scanningdirection is represented by a function up to the 6th order andsub-scanning direction is represented by a 2nd-order phase functionwhich changes depending on the position of the main scanning direction,which is represented by

φ=mλ=b₂Y²+b₄Y⁴+b₆Y⁶ +(d₀+d₁Y+d₂Y^(2+d) ₃Y³+d₄Y⁴)Z²

(where m is the order of diffraction, and+1st-order diffracted light isused in the first to third embodiments)

Table-1 shows the optical layout in the first embodiment, asphericalcoefficients of the toric lens 61, and phase terms of the diffractiveoptical element 62. In Table-1, the depth of the diffraction grating ish=1.51 μm, the angle of incidence of an off-axis light component on thediffraction grating is θi=22°, and the grating pitch is P=5.6 μm.

TABLE 1 First Embodiment Design Data Wavelength, Refractive IndexWavelength Used λ (nm) 780 Refractive Index of Toric Lens 61 nt 1.5242Refractive Index of Elongated Diffractive nd 1.5242 Element 62 Light RayAngle Angle of Incidence on Polygon θp 70.0 Polygon Maximum Exit Angleθe 45.0 Maximum Angle of Incidence on Surface θi 25.0 to be ScannedLayout Polygon Axis - Toric Lens e1 36.4 Toric Lens Central Thickness d111.0 Toric Lens - Elongated diffractive Element e2 86.0 ElongatedDiffractive Element Central d2 3.0 Thickness Elongated DiffractiveElement - Surface to Sk 110.0 be Scanned Polygon Axis - Surface to beScanned L 246.4 Effective Scanning Width W 297.0 First Surface SecondSurface Surface Shape of Toric Lens 61 R −1.41591E + 02 −6.18036E + 01 K 5.27866E + 00 −6.46577E − 01 B4  1.21014E − 06  4.20445E − 07 B6 7.51335E − 11  2.81267E − 10 r  1.44405E + 02 −2.51589E + 01 D2a 1.75165E − 04 D4s −3.02404E − 08 D6s  3.83856E − 11 D2e  2.46819E − 04D4e −9.77441E − 08 D6e  7.36681E − 11 Suffices s indicate laser sideSuffices e indicate side opposite to laser Surface Shape of ElongatedDiffractive Element 62 R ∞ ∞ K B4 B6 Phase Function of ElongatedDiffractive Element 62 b2 −2.50725E − 04 b4 −4.31479E − 08 b6  1.23655E− 12 d0 −5.78930E − 03 d1 −9.57598E − 07 d2  1.15549E − 07 d3  3.71159E− 11 d4  1.23655E − 12

FIG. 7 is a sectional view showing a principal part of the diffractiveoptical element of the first embodiment in the main scanning direction.FIG. 7 shows an enlarged grating portion. Referring to FIG. 7, adiffraction grating 11 comprises a tilt portion 31 for mainly generatinga power, and a wall portion 32 connecting one end portion 31 a of thetilt portion 31 to a substrate 22. The wall portion 32 is tilted withrespect to the normal (to be referred to as a substrate normalhereinafter) to the surface of the substrate 22 by a tilt angle θe. Inthis embodiment, the tilt angle θe of the wall portion 32 with respectto the substrate normal is set to satisfy a relation

θe=tan⁻¹(h/P)

where h is the depth of the diffraction grating 11, and P is the gratingpitch. The tilt angle θe is continuously changed to increase as thedistance from the optical axis of the diffractive optical element 62becomes large. This means that the tilt portion 31 and wall portion 32of the diffraction grating 11 always make a right angle.

In this embodiment, the tilt angle θe of the wall portion 32 withrespect to the substrate normal is continuously changed to increase asthe distance from the optical axis of the diffractive optical element 62becomes large. However, the tilt angle θe may be intermittently changed.

FIG. 8 is an explanatory view showing the diffraction efficiency whenthe diffractive optical element 62 of the first embodiment is used on anapparatus. The abscissa is converted into a light beam arrival positionon the surface to be scanned. The diffraction efficiency is calculatedin consideration of the angle of incidence, aspect ratio, tilt angle ofthe grating wall portion, and the like at each light beam passageposition.

Referring to FIG. 8, a solid line “a” indicates the diffractionefficiency in the first embodiment, which is obtained when the wallportion is tilted with respect to the substrate normal by θe=tan⁻¹(h/P).A dotted line “b” indicates a conventional diffraction efficiencyobtained when the wall portion is formed perpendicular to the substratesurface.

As is apparent from FIG. 8, when the wall portion of the diffractiongrating is tilted with respect to the substrate normal by θe, thediffraction efficiency in the off-axis region can be improved by about11.7%.

As described above, in the first embodiment, with a simple arrangementin which the diffraction grating 11 of the diffractive optical element62 comprises the tilt portion 31 and wall portion 32, and the wallportion 32 is tilted with respect to the substrate normal, a decrease indiffraction efficiency due to a large angle of incidence in the off-axisregion and low aspect ratio, which poses a problem in use of thediffractive optical element 62 in a scanning optical apparatus, can besuppressed. Hence, a scanning optical apparatus (image formingapparatus) suitable for high-resolution printing, which increases theuniformity of image plane illuminance on the surface to be scanned inthe scanning optical apparatus and minimizes aberration changes due tovarious variations can be realized.

As the characteristic feature unique to the first embodiment, when thetilt angle of the wall portion 32 with respect to the substrate normalis set as θe=tan⁻¹(h/P), the tilt portion 31 and wall portion 32 of thediffraction grating 11 always make a right angle. Hence, the diffractiongrating or its mold can be considerably easily manufactured.

FIG. 9 is a sectional view showing a principal part of a diffractiveoptical element according to the second embodiment of the presentinvention in the main scanning direction. FIG. 9 shows an enlargedgrating portion. The same reference numerals as in FIG. 7 denote thesame elements in FIG. 9.

The second embodiment is different from the above-described firstembodiment in that a tilt angle θe of a wall portion 52 of a diffractiongrating 12 with respect to the substrate normal is changed. Thearrangement of remaining portions and optical function are substantiallythe same as in the first embodiment, and the same effect as in the firstembodiment is obtained.

More specifically, the diffraction grating 12 of the second embodimentcomprises a tilt portion 51 for mainly generating a power and the wallportion 52 connecting one end portion 51 a of the tilt portion 51 to asubstrate 22, as shown in FIG. 9. The wall portion 52 is tilted withrespect to the substrate normal by the tilt angle θe. In thisembodiment, the tilt angle θe of the wall portion 52 with respect to thesubstrate normal is set to satisfy a relation

θe=tan⁻¹(h/P)+5°

where h is the depth of the diffraction grating 12, and P is the gratingpitch. The tilt angle θe is continuously changed to increase as thedistance from the optical axis of a diffractive optical element 64becomes large.

FIG. 10 is an explanatory view showing the diffraction efficiency whenthe diffractive optical element 64 of the second embodiment is used onan apparatus. The abscissa is converted into a light beam arrivalposition on the surface to be scanned. The diffraction efficiency iscalculated in consideration of the angle of incidence, aspect ratio,tilt angle of the grating wall portion, and the like at each light beampassage position.

Referring to FIG. 10, a solid line “a” indicates the diffractionefficiency in the second embodiment, which is obtained when the wallportion is tilted with respect to the substrate normal byθe=tan⁻¹(h/P)+5°. A dotted line “b” indicates a conventional diffractionefficiency obtained when the wall portion is formed perpendicular to thesubstrate surface.

As is apparent from FIG. 10, when the wall portion of the diffractiongrating is tilted with respect to the substrate normal by θe, thediffraction efficiency in the off-axis region can be improved by about11.1%.

As described above, in the second embodiment, with a simple arrangementin which the diffraction grating 12 of the diffractive optical element64 comprises the tilt portion 51 and wall portion 52, and the wallportion 52 is tilted with respect to the substrate normal, a decrease indiffraction efficiency due to a large angle of incidence in the off-axisregion and low aspect ratio, which poses a problem in the use of thediffractive optical element 64 in a scanning optical apparatus, can besuppressed. Hence, a scanning optical apparatus (image formingapparatus) suitable for high-resolution printing, which increases theuniformity of image plane illuminance on the surface to be scanned inthe scanning optical apparatus and minimizes aberration changes due tovarious variations can be realized.

As the characteristic feature unique to the second embodiment, when thetilt angle of the wall portion 52 with respect to the substrate normalis set as θe=tan⁻¹(h/P)+50°, the tilt portion 51 and wall portion 52 ofthe diffraction grating 12 always make an obtuse angle (95°). Since thewall portion 52 of the diffraction grating 12 can be tilted even at alarge pitch portion near the on-axis region, mold releasecharacteristics in injection molding or replica are improved, and thediffraction efficiency can be prevented from lowering due to errors inmanufacturing.

FIG. 11 is a sectional view showing a principal part of the opticalsystem of a scanning optical apparatus according to the third embodimentof the present invention in the main scanning direction. FIG. 12 is asectional view showing principal part of a diffractive optical elementshown in FIG. 11 in the main scanning direction. FIG. 12 shows anenlarged grating portion. The same reference numerals as in FIG. 6denote the same elements in FIG. 11.

The third embodiment is different from the above-described firstembodiment in that an elongated diffractive optical element 63 having acurved substrate surface is used. The arrangement of remaining portionsand optical function are substantially the same as in the firstembodiment, and the same effect as in the first embodiment is obtained.

More specifically, a diffraction grating 13 of the third embodimentcomprises a tilt portion 81 for mainly generating a power and a wallportion 82 connecting one end portion 81 a of the tilt portion 81 to asubstrate 42, as shown in FIG. 12. The wall portion 82 is tilted withrespect to the substrate normal by a tilt angle θe. In this embodiment,the tilt angle θe of the wall portion 82 with respect to the substratenormal is set to satisfy a relation

θe=tan⁻¹(h/P)

where h is the depth of the diffraction grating 13, and P is the gratingpitch. The tilt angle θe is continuously changed to increase as thedistance from the optical axis of the diffractive optical element 63becomes large. This embodiment has the same effect as that when thesubstrate surface is flat and can improve the diffraction efficiency inthe off-axis region as compared to a case wherein the wall portion ofthe diffraction grating is formed perpendicular to the substratesurface.

Table-2 shows the optical layout in the third embodiment, asphericalcoefficients of a toric lens 71, and phase terms of the diffractiveoptical element 63. In Table-2, the depth of the diffraction grating ish=1.51 μm, the angle of incidence of an outermost off-axis lightcomponent on the diffraction grating is θi=22°, and the grating pitch isP=5.6 μm.

TABLE 2 Third Embodiment Design Data Wavelength, Refractive IndexWavelength Used λ (nm) 780 Refractive Index of Toric Lens 71 nt 1.5242Refractive Index of Elongated Diffractive nd 1.5242 Element 63 Light RayAngle Angle of Incidence on Polygon θp 70.0 Polygon Maximum Exit Angleθe 45.0 Maximum Angle of Incidence on Surface to θi 23.0 be ScannedLayout Polygon Axis - Toric Lens e1 36.4 Toric Lens 71 Central Thicknessd1 11.0 Toric Lens - Elongated Diffractive Element e2 90.5 ElongatedDiffractive Element 63 Central d2 4.0 Thickness Elongated DiffractiveElement - Surface to Sk 104.5 be Scanned Polygon Axis - Surface to beScanned L 246.4 Effective Scanning Width W 297.0 First Surface SecondSurface Surface Shape of Toric Lens 71 R −1.06291E + 02 −5.37548E + 01 K−3.31352E − 01 −9.34202E − 01 B4  1.30030E − 06  2.51064E − 07 B6−7.62356E − 11  2.80118E − 10 r  1.55072E + 02 −2.40083E + 01 D2s 1.47931E − 04 D4s  5.78375E − 08 D6s −1.06573E − 11 D2e  2.23682E − 04D4e −1.29434E − 08 D6e  2.62146E − 11 Surface Shape of ElongatedDiffractive Element 63 R −4.33451E + 02 −1.72797E + 03 K −1.19232E + 00 6.06107E + 00 B4  3.14632E − 08 −5.49468E + 08 B6  1.09311E − 12 3.42409E − 12 Phase Function of Elongated Diffractive Element 63 b2−5.79065E − 04 b4 −1.13552E − 08 b6  3.59430E − 13 d0 −5.73306E − 03 d1−9.14465E − 07 d2  8.78326E − 08 d3  3.06812E − 11 d4 −8.98137E − 13

As described above, in the third embodiment, with a simple arrangementin which the diffraction grating 13 of the diffractive optical element63 comprises the tilt portion 81 and wall portion 82, and the wallportion 82 is tilted with respect to the substrate normal, a decrease indiffraction efficiency due to a large angle of incidence in the off-axisregion and low aspect ratio, which poses a problem in use of thediffractive optical element 63 in a scanning optical apparatus, can besuppressed. Hence, a scanning optical apparatus (image formingapparatus) suitable for high-resolution printing, which increases theuniformity of image plane illuminance on the surface to be scanned inthe scanning optical apparatus and minimizes aberration changes due tovarious variations can be realized.

The tilt angle θe of the wall portion of the diffraction grating withrespect to the substrate normal is set as θe=tan⁻¹(h/P) in the first andthird embodiments, and θe=tan⁻¹(h/P)+50° in the second embodiment. Whencondition (1) below is satisfied, the present invention can be appliedas in the first, second, and third embodiments.

tan⁻¹(h/P)≦θe≦tan⁻¹(h/P)+10°  (1)

Condition (1) defines the tilt angle of the wall portion of thediffraction grating with respect to the substrate normal. When condition(1) is not satisfied, the diffraction efficiency lowers in the off-axisregion where the angle of incidence is large and aspect ratio is low,and the uniformity of image plane illuminance on the surface to bescanned degrades.

According to the present invention, the diffraction grating of adiffractive optical element is formed from a tilt portion for mainlygenerating a power and a wall portion connecting one end portion of thetilt portion to a substrate, and the wall portion is tilted with respectto the normal of the substrate surface. Hence, a diffractive opticalelement suitable for high-resolution printing, which suppresses adecrease in diffraction efficiency of the diffractive optical elementespecially in the off-axis region, increases the uniformity of imageplane illuminance on a surface to be scanned, and minimizes aberrationchanges due to various variations with the simple arrangement withoutincreasing cost and a scanning optical apparatus using the same can beprovided.

What is claimed is:
 1. A scanning optical apparatus comprising: a lightsource; a conversion optical element for converting a light beam emittedby said light source into a substantially collimated light beam; adeflection element for deflecting the converted substantially collimatedlight beam; and a scanning optical element for forming an image of thelight beam deflected by said deflection element on a surface to bescanned, wherein said scanning optical element comprises at least onerefractive optical element and at least one diffractive optical elementhaving a diffraction grating, said diffraction grating being formed on asubstrate surface and having a tilt portion for generating power and awall portion connecting one end portion of said tilt portion to thesubstrate, and said wall portion being tilted with respect to a normalto the substrate surface, and a tilt angle θe of said wall portion withrespect to the normal to the substrate surface continuously changes toincrease as a distance from an optical axis of said diffractive opticalelement becomes large.
 2. An apparatus according to claim 1, wherein thediffraction grating is formed on a side of the surface to be scanned ofsaid diffractive optical element.
 3. An apparatus according to claim 1,wherein a tilt angle θe of said wall portion of said diffraction gratingwith respect to the normal to the substrate surface satisfiestan⁻¹(h/P)≦θe≦tan⁻¹(h/P)+10°  where h is a depth of said diffractiongrating, and P is a grating pitch.
 4. An apparatus according to claim 1,wherein said diffractive optical element is manufactured by forming saiddiffraction grating on a glass substrate by a replica process.
 5. Anapparatus according to claim 1, wherein said diffractive optical elementis manufactured by integrally forming the substrate and said diffractiongrating from plastic material by injection molding.
 6. An apparatusaccording to claim 1, wherein said refractive optical element comprisesa toric lens made of plastic and has different powers in main scanningand sub-scanning directions.
 7. An apparatus according to claim 1,wherein said substrate surface comprises a flat surface or a curvedsurface.